In addition, the prime minister said possessing online pornography depicting rape would become illegal in England and Wales - in line with Scotland.
Mr Cameron warned in a speech that access to online pornography was "corroding childhood".
The new measures will apply to both existing and new customers.
Mr Cameron also called for some "horrific" internet search terms to be "blacklisted", meaning they would automatically bring up no results on websites such as Google or Bing.
He told the BBC he expected a "row" with service providers who, he said in his speech, were "not doing enough to take responsibility" despite having a "moral duty" to do so.
He also warned he could have to "force action" by changing the law and that, if there were "technical obstacles", firms should use their "greatest brains" to overcome them.
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